Beam Deflection Calculator

Beam deflection is the displacement produced when a transverse load bends a structural member. This calculator handles two fundamental idealized cases: a simply supported beam with a point load at midspan and a cantilever beam with a point load at its free end. For either case, it reports maximum elastic deflection, maximum bending moment, and nominal bending stress. These cases are useful for learning, preliminary sizing, and checking a hand calculation before more detailed analysis. For a simply supported beam carrying a center point load, maximum deflection equals load times length cubed divided by forty-eight times elastic modulus times second moment of area. Maximum moment equals load times length divided by four. For a cantilever with an end point load, maximum deflection equals load times length cubed divided by three times elastic modulus times second moment of area, while maximum moment equals load times length. Nominal bending stress equals maximum moment divided by section modulus. The inputs use a coherent SI system: newtons, meters, pascals, meters to the fourth power, and meters cubed. The displayed deflection is converted to millimeters, moment remains in newton-meters, and stress is converted to megapascals. Elastic modulus describes material stiffness. Moment of inertia describes cross-section stiffness about the bending axis, while section modulus connects bending moment to extreme-fiber stress. Manufacturer tables or verified section-property calculations are preferable to rough estimates. These closed-form equations assume a straight, prismatic beam, small deflection, linear elastic material, ideal supports, and a static point load at the specified location. They omit self-weight, distributed loads, lateral torsional buckling, shear deformation, connection flexibility, holes, notches, composite behavior, vibration, fatigue, and load combinations. Real design also requires strength reduction factors, serviceability limits, stability checks, and applicable building standards. Use the calculator as an educational and preliminary analysis tool only. Have a licensed structural professional verify any beam whose failure could damage property or injure people.